The Elements in Nature and Industry

A major use of ${\text{Cl}}_{\text{2}}$  is in the manufacture of vinyl chloride, the monomer of poly (vinyl chloride). The two-step sequence for formation of vinyl chloride is depicted below.

(a) Write a balanced equation for each step. 

(b) Write the overall equation. 

(c) What type of organic reaction is shown in step  1? 

(d) What type of organic reaction is shown in step  2? 

(e) If each molecule depicted in the initial reaction mixture represents 0.15 mol of substance, what mass (in $g$ ) of vinyl chloride forms?

Why is commercial ${\mathbf{\text{H}}}_{\mathbf{\text{2}}}{\mathbf{\text{SO}}}_{\mathbf{\text{4}}}$ so inexpensive? 

(a) What are the three commercial products formed in the chlor-alkali process? 

(b) State an advantage and a disadvantage of the mercury-cell method for this process.

For the reaction of ${\mathbf{\text{SO}}}_{\mathbf{\text{2}}}{\mathbf{\text{ to SO}}}_{\mathbf{\text{3}}}$ at standard conditions, 

(a) Calculate ${\mathbf{\Delta G}}^{\mathbf{0}}\mathbf{ }\mathbf{at}\mathbf{ }{\mathbf{25}}^{\mathbf{0}}\mathbf{C}\mathbf{.}$ Is the reaction spontaneous? 

(b) Why is the reaction not performed at ${\mathbf{25}}^{\mathbf{0}}\mathbf{C}$? 

(c) Is the reaction spontaneous at ${\mathbf{500}}^{\mathbf{0}}\mathbf{C}$ ? (Assume ${\mathbf{\Delta H}}^{\mathbf{0}}\mathbf{ }\mathbf{and}\mathbf{ }{\mathbf{\Delta S}}^{\mathbf{0}}$ are constant with changing  T.) 

(d) Compare $\mathbf{K}\mathbf{ }\mathbf{at}\mathbf{ }{\mathbf{500}}^{\mathbf{0}}\mathbf{C}\mathbf{ }\mathbf{and}\mathbf{ }\mathbf{at}\mathbf{ }{\mathbf{25}}^{\mathbf{0}}\mathbf{C}$ 

(e) What is the highest T at which the reaction is spontaneous?

If a chlor-alkali cell used a current of $\mathbf{3}\mathbf{\times }{\mathbf{10}}^{\mathbf{4}}\mathbf{ }\mathbf{A}$, how many how many pounds of ${\mathbf{\text{Cl}}}_{\mathbf{\text{2}}}$ would be produced in a typical $\mathbf{\text{8 - h}}$ operating day?

In the production of magnesium, ${\mathbf{\text{Mg(OH)}}}_{\mathbf{\text{2}}}$  is precipitated by using  ${\mathbf{\text{Ca(OH)}}}_{\mathbf{\text{2}}}$, which itself is “insoluble.” 

(a) Use ${\mathbf{\text{K}}}_{\mathbf{\text{sp}}}$  values to show that  ${\mathbf{\text{Mg(OH)}}}_{\mathbf{\text{2}}}$ can be precipitated from seawater in which  ${\mathbf{\text{[Mg}}}^{\mathbf{\text{2 + }}}\mathbf{\text{]}}$ is initially 0.052M. 

(b) If the seawater is saturated with  ${\mathbf{\text{Ca(OH)}}}_{\mathbf{\text{2}}}$, what fraction of the ${\mathbf{\text{[Mg}}}^{\mathbf{\text{2 + }}}\mathbf{\text{]}}$  is precipitated?

The Ostwald process for the production of ${\mathbf{\text{HNO}}}_{\mathbf{\text{3}}}$  is 

   $$\begin{gathered} {\mathbf{\text{(1)4NH}}}_{\mathbf{\text{3}}}{\mathbf{\text{(g) + 5O}}}_{\mathbf{\text{2}}}\mathbf{\text{(g)}}\stackrel{\mathbf{\text{Pt/Rh Catalyst}}}{\mathbf{\to }}{\mathbf{\text{4NO(g) + 6H}}}_{\mathbf{\text{2}}}\mathbf{\text{O(g)}} \\ {\mathbf{\text{(2)2NO(g) + O}}}_{\mathbf{\text{2}}}\mathbf{\text{(g)}}\mathbf{\to }{\mathbf{\text{2NO}}}_{\mathbf{\text{2}}}\mathbf{\text{(g)}} \\ {\mathbf{\text{(3)3NO}}}_{\mathbf{\text{2}}}{\mathbf{\text{(g) + H}}}_{\mathbf{\text{2}}}\mathbf{\text{O(l)}}\mathbf{\to }{\mathbf{\text{2HNO}}}_{\mathbf{\text{3}}}\mathbf{\text{(aq) + NO(g)}} \end{gathered}$$

(a) Describe the nature of the change that occurs in step  . 

(b) Write an overall equation that includes  ${\mathbf{\text{NH}}}_{\mathbf{\text{3}}}$ and  ${\mathbf{\text{HNO}}}_{\mathbf{\text{3}}}$ as the only nitrogen-containing species.

(c) Calculate $\mathit{\Delta }{\mathit{H}}_{\mathbf{r}\mathbf{x}\mathbf{n}}^{\mathbf{o}}$  (in kJ/mol   atoms) for this reaction at   ${\mathbf{\text{25}}}^{\mathbf{\text{o}}}\mathbf{\text{C}}$.

Explain in detail why a catalyst is used to produce ${\mathbf{\text{SO}}}_{\mathbf{\text{3}}}$.

Use equations to show how acid-base properties are used to separate ${\mathbf{\text{Fe}}}_{\mathbf{\text{2}}}{\mathbf{\text{O}}}_{\mathbf{\text{3}}}$and ${\mathbf{\text{TiO}}}_{\mathbf{\text{2 }}}{\mathbf{\text{from Al}}}_{\mathbf{\text{2}}}{\mathbf{\text{O}}}_{\mathbf{\text{3}}}$ in the Bayer process.

Metal sulfides are often first converted to oxides by roasting in air and then reduced with carbon to produce the metal. Why aren’t the metal sulfides reduced directly by carbon to yield${\mathbf{\text{CS}}}_{\mathbf{\text{2}}}$? Give a thermodynamic analysis of both processes for$\mathbf{\text{ZnS}}$ .

In the 1980 s, U.S. Fish and Wildlife Service researchers found high mortality among newbem coots and ducks in parts of California. U.S. Geological Survey scientists later found the cause to be a high selenium concentration agricultural drainage water. 

Balance these half-reactions in the selenium cycle:

$$\begin{gathered} \mathbf{\left(}\mathit{a}\mathbf{\right)}{\mathbf{\text{Se}}}^{\mathbf{2}\mathbf{-}}\left(aq\right)\mathbf{\to }\mathbf{\text{Se}}\mathbf{\left(}\mathit{s}\mathbf{\right)} \\ \mathbf{\left(}\mathit{b}\mathbf{\right)}{\mathbf{\text{SeO}}}_{\mathbf{3}}^{\mathbf{2}\mathbf{-}}\mathbf{\left(}\mathit{a}\mathit{q}\mathbf{\right)}\mathbf{\to }{\mathbf{\text{SeO}}}_{\mathbf{4}}^{\mathbf{2}\mathbf{-}}\mathbf{\left(}\mathit{a}\mathit{q}\mathbf{\right)} \\ \mathbf{\left(}\mathit{c}\mathbf{\right)}{\mathbf{\text{SeO}}}_{\mathbf{4}}^{\mathbf{2}}\mathbf{\left(}\mathit{a}\mathit{q}\mathbf{\right)}\mathbf{\to }\mathbf{\text{Se}}\mathbf{\left(}\mathbf{\text{s}}\mathbf{\right)} \end{gathered}$$

A key part of the carbon cycle is the fixation of  ${\mathbf{\text{CO}}}_{\mathbf{\text{2}}}$ by photosynthesis to produce carbohydrates and oxygen gas. 

(a) Using the formula $\mathbf{(}\mathit{C}{\mathit{H}}_{\mathbf{2}}\mathit{O}{\mathbf{)}}_{\mathbf{\text{n}}}$  to represent a carbohydrate, write a balanced equation for the photosynthetic reaction. 

(b) If a tree fixes $\mathbf{\text{48 g}}$  of  $\mathit{C}{\mathit{O}}_{\mathbf{2}}$ per day, what volume of  ${\mathit{O}}_2$ gas measured at   $\mathbf{\text{1.0 atm}}$and ${\mathbf{\text{78}}}^{\mathbf{\text{o}}}\mathbf{\text{F}}$  does the tree produce per day? 

(c) What volume of air ( ${\mathbf{\text{0.035 mol \% CO}}}_{\mathbf{\text{2}}}$) at the same conditions contains this amount of ${\mathbf{\text{CO}}}_{\mathbf{\text{2}}}$ ?

Nitric oxide occurs in the tropospheric nitrogen cycle, but it destroys ozone in the stratosphere. 

(a) Write equations for its reaction with ozone and for the reverse reaction. 

(b) Given tha$\mathbf{∆}{\mathit{G}}^{\mathbf{°}}$t the forward and reverse steps are first order in each component, write general rate laws for them. 

(c) Calculate for this reaction at$\mathbf{\text{280 K}}$ , the average temperature in the stratosphere. (Assume that the $\mathbf{∆}{\mathit{H}}^{\mathbf{°}}$and ${\mathit{S}}^{\mathbf{°}}$values in Appendix B do not change with temperature.) 

(d) What ratio of rate constants is consistent with$\mathit{K}$ at this temperature

When gold ores are leached with   solutions, gold forms a complex ion, $\mathbf{\text{Au(CN}}{{\mathbf{\text{)}}}_{\mathbf{\text{2}}}}^{\mathbf{\text{ - }}}$ , (a) Find  ${\mathbf{\text{E}}}_{\mathbf{\text{cell }}}$ for the oxidation in air $\left({\text{P}}_{{\text{O}}_{\text{2}}}\text{ = 0.2l}\right)$  of ${\mathbf{\text{Au}}}^{}$ to ${\mathbf{\text{Au}}}^{\mathbf{\text{ + }}}$  in basic   $\mathbf{\text{(pH13.55)}}$solution with $\left[{\text{Au}}^{\text{ + }}\right]\mathbf{\text{ = 0.50M}}$  Is the reaction${\mathbf{\text{Au}}}^{\mathbf{\text{ + }}}{\mathbf{\text{(aq) + e}}}^{\mathbf{\text{ - }}}\mathbf{\to }\mathbf{\text{Au(s)}}$  ${\mathit{E}}^{\mathbf{°}}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{68}\mathit{V}$ spontaneous? (b) How does formation of the complex ion change   so that the oxidation can be accomplished?

Before the development of the Downs cell, the Castner cell was used for the industrial production of  metal. The Castner cell was based on the electrolysis of molten$\mathbf{\text{NaOH}}$  ,

(a) Write balanced cathode and anode half-reactions for this cell.

(b) A major problem with this cell was that the water produced at one electrode diffused to the other and reacted with the Na. If all the water produced reacted with  , what would be the maximum efficiency of the Castner cell expressed as moles of Na produced per mole of electrons flowing through the cell?

Below ${\mathbf{912}}^{\mathbf{°}}\mathit{C}$,pure iron crystallizes in a body-centered cubic structure (ferrite) with a density of ${\mathbf{\text{7.86 g/cm}}}^{\mathbf{\text{3}}}$ ; from${\mathbf{912}}^{\mathbf{°}}\mathit{C}$ to ${\mathbf{1394}}^{\mathbf{°}}\mathit{C}$, it adopts a face-centered cubic structure (austenite) with a density of$\mathbf{\text{7.40 g/cm}}$ . Both types of iron form interstitial alloys with carbon. The maximum amount of carbon is 0.0218mass$\mathbf{\%}$ in ferrite and 2.08mass$\mathbf{\%}$  in austenite. Calculate the density of each alloy.

The key reaction (unbalanced) in the manufacture of synthetic cryolite for aluminum electrolysis is

 $\mathbf{\text{HF}}\mathbf{\left(}\mathbf{\text{g}}\mathbf{\right)}\mathbf{+}\mathbf{\text{Al}}\mathbf{(}\mathbf{\text{OH}}{\mathbf{)}}_{\mathbf{3}}\mathbf{\left(}\mathit{s}\mathbf{\right)}\mathbf{+}\mathbf{\text{NaOH}}\mathbf{\left(}\mathit{a}\mathit{q}\mathbf{\right)}\mathbf{\to }{\mathbf{\text{Na}}}_{\mathbf{3}}{\mathbf{\text{AlF}}}_{\mathbf{6}}\mathbf{\left(}\mathit{a}\mathit{q}\mathbf{\right)}\mathbf{+}{\mathbf{\text{H}}}_{\mathbf{2}}\mathbf{\text{O}}\mathbf{\left(}\mathit{\ell }\mathbf{\right)}$

Assuming a$\mathbf{\text{95.6\% }}$  yield of dried, crystallized product, what mass (in  ) of cryolite can be obtained from the reaction of  $\mathbf{365}\mathit{k}\mathit{g}$of ${\mathbf{\text{Al(OH)}}}_{\mathbf{\text{3}}}$, $\mathbf{1}\mathbf{.}\mathbf{20}\mathbf{ }{\mathit{m}}^{\mathbf{3}}$  of$\mathbf{\text{50.0\% }}$  by mass aqueous  $\mathit{N}\mathit{a}\mathit{O}\mathit{H}\mathbf{(}\mathit{d}\mathbf{ }\mathbf{=}\mathbf{ }\mathbf{1}\mathbf{.}\mathbf{53}\mathit{g}\mathbf{/}\mathit{m}\mathit{l}\mathbf{)}$, and  ${\mathbf{\text{265m}}}^{\mathbf{\text{3}}}$ of gaseous HF  $\mathbf{\text{305kP}}$ and $\mathbf{91}\mathbf{.}{\mathbf{5}}^{\mathbf{°}}\mathit{C}$  (Assume that the ideal gas law holds)

Farmers use ammonium sulfate as a fertilizer. In the soil, nitrifying bacteria oxidize  $\mathbf{\text{N}}{{\mathbf{\text{H}}}_{\mathbf{\text{4}}}}^{\mathbf{\text{ + }}}$$\mathbf{\text{N}}{{\mathbf{\text{O}}}_{\mathbf{\text{3}}}}^{\mathbf{\text{ - }}}$a groundwater contaminant that causes methemoglobinemia ("blue baby" syndrome). The World Health Organization standard for maximum $\left[\text{N}{{\text{O}}_{\text{3}}}^{\text{ - }}\right]$ in groundwater is $\mathbf{\text{45mg/L}}$ . A farmer adds  $\mathbf{\text{210.kg}}$ of  ${\left({\text{NH}}_{\text{4}}\right)}_{\mathbf{\text{2}}}$${\mathbf{\text{SO}}}_{\mathbf{\text{4}}}$ to a field and $\mathbf{\text{37\% }}$ is oxidized to $\mathbf{\text{N}}{{\mathbf{\text{O}}}_{\mathbf{\text{3}}}}^{\mathbf{\text{ - }}}$ What is the groundwater $\mathbf{\text{(inmg/L)}}$  if ${\mathbf{\text{1000.m}}}^{\mathbf{\text{3}}}$f the water is contaminated?

Why isn't nitric acid produced by oxidizing  ${\mathit{N}}_{\mathbf{2}}$ as follows?

$$\begin{gathered} \mathbf{\left(}\mathbf{1}\mathbf{\right)}{\mathbf{\text{N}}}_{\mathbf{2}}\mathbf{\left(}\mathit{g}\mathbf{\right)}\mathbf{+}\mathbf{2}{\mathbf{\text{O}}}_{\mathbf{2}}\mathbf{\left(}\mathit{g}\mathbf{\right)}\mathbf{\to }\mathbf{2}{\mathbf{\text{NO}}}_{\mathbf{2}}\mathbf{\left(}\mathit{g}\mathbf{\right)} \\ \mathbf{\left(}\mathbf{2}\mathbf{\right)}\mathbf{3}{\mathbf{\text{NO}}}_{\mathbf{2}}\mathbf{\left(}\mathit{g}\mathbf{\right)}\mathbf{+}{\mathbf{\text{H}}}_{\mathbf{2}}\mathbf{\text{O}}\mathbf{\left(}\mathit{l}\mathbf{\right)}\mathbf{\to }\mathbf{2}{\mathbf{\text{HNO}}}_{\mathbf{3}}\mathbf{\left(}\mathit{a}\mathit{q}\mathbf{\right)}\mathbf{+}\mathbf{\text{NO}}\mathbf{\left(}\mathit{g}\mathbf{\right)} \\ \mathbf{\left(}\mathbf{3}\mathbf{\right)}\frac{\mathbf{2}\mathbf{\text{NO}}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{+}{\mathbf{\text{O}}}_{\mathbf{2}}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{\to }\mathbf{2}{\mathbf{\text{NO}}}_{\mathbf{2}}\mathbf{\left(}\mathbf{g}\mathbf{\right)}}{\mathbf{3}\mathbf{ }{\mathbf{\text{N}}}_{\mathbf{2}}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{+}\mathbf{6}{\mathbf{\text{O}}}_{\mathbf{2}}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{+}\mathbf{2}{\mathbf{\text{H}}}_{\mathbf{2}}\mathbf{\text{O}}\mathbf{\left(}\mathbf{l}\mathbf{\right)}\mathbf{\to }\mathbf{4}{\mathbf{\text{HNO}}}_{\mathbf{3}}\mathbf{\left(}\mathbf{a}\mathbf{q}\mathbf{\right)}\mathbf{+}\mathbf{2}\mathbf{\text{NO}}\mathbf{\left(}\mathbf{g}\mathbf{\right)}} \end{gathered}$$

Step  1 of the Ostwald process for nitric acid production is 

  ${\mathbf{\text{4NH}}}_{\mathbf{\text{3}}}{\mathbf{\text{(g) + 5O}}}_{\mathbf{\text{2}}}\mathbf{\text{(g)}}\stackrel{\mathbf{\text{Pt/Rh Catalyst}}}{\mathbf{\to }}{\mathbf{\text{4NO(g) + 6H}}}_{\mathbf{\text{2}}}\mathbf{\text{O(g)}}$

An unwanted side reaction for this step is 

  ${\mathbf{\text{4NH}}}_{\mathbf{\text{3}}}{\mathbf{\text{(g) + 3O}}}_{\mathbf{\text{2}}}\mathbf{\text{(g)}}\mathbf{\to }{\mathbf{\text{2N}}}_{\mathbf{\text{2}}}{\mathbf{\text{(g) + 6H}}}_{\mathbf{\text{2}}}\mathbf{\text{O(g)}}$

(a) Calculate  ${\mathbf{\text{K}}}_{\mathbf{p}}$ for these two  ${\mathbf{\text{NH}}}_{\mathbf{\text{3}}}$ oxidations at  ${\mathbf{\text{25}}}^{\mathbf{\text{o}}}\mathbf{\text{C}}$. 

(b) Calculate ${\mathbf{\text{K}}}_{\mathbf{p}}$  for these two ${\mathbf{\text{NH}}}_{\mathbf{\text{3}}}$  oxidations at  ${\mathbf{\text{900}}}^{\mathbf{\text{o}}}\mathbf{\text{C}}$.

(c) The  $\mathbf{\text{Pt/Rh}}$ catalyst is one of the most efficient in the chemical industry, achieving 96%  yield in   millisecond of contact with the reactants. However, at normal operating conditions ( 5 atm and ${\text{850}}^{\text{∘}}\text{C}$ ), about  175 mg of   is lost per metric ton ( $\mathit{t}$) of  ${\mathbf{\text{HNO}}}_{\mathbf{\text{3}}}$ produced. If the annual U.S. production of  ${\mathbf{\text{HNO}}}_{\mathbf{\text{3}}}$ is  $\mathbf{1}\mathbf{.}\mathbf{01}\mathbf{\times }{\mathbf{10}}^{\mathbf{7}}\mathit{t}$ and the market price of  $\mathit{P}\mathit{t}$ is  $\mathbf{\$}\mathbf{1260}\mathbf{/}\mathit{t}\mathit{r}\mathit{o}\mathit{y}\mathit{o}\mathit{z}$, what is the annual cost of the lost   ( $\mathbf{1}\mathit{k}\mathit{g}\mathbf{=}\mathbf{32}\mathbf{.}\mathbf{15}\mathit{t}\mathit{r}\mathit{o}\mathit{y}\mathit{o}\mathit{z}$)?

(d) Because of the high price of  $\mathit{P}\mathit{t}$, a filtering unit composed of ceramic fibre is often installed, which recovers as much as  75% of the lost  $\mathit{P}\mathit{t}$. What is the value of the  $\mathit{P}\mathit{t}$ captured by a recovery unit with 72% efficiency?

The compounds ${\left({\mathrm{NH}}_4\right)}_{\mathbf{2}}{\mathbf{HPO}}_{\mathbf{4}}$ and ${\mathbf{NH}}_{\mathbf{4}}\left(H_2{\mathrm{PO}}_4\right)$  are water-soluble fertilizers. 

(a) Which has the higher mass $\mathbf{\%}$  of   $\mathbf{P}$? 

(b) Why might the one with the lower mass $\mathbf{\%}$  of $\mathbf{P}$ be preferred?

Several transition metals are prepared by reduction of the metal halide with magnesium. Titanium is prepared by the Kroll method, in which ore (ilmenite) is converted to the gaseous chloride, which is then reduced to  metal by molten Mg(see p. 1008). Assuming yields of 84% for step 1 and 93% for step 2, and an excess of the other reactants, what mass of Ti metal can be prepared from 21.5 metric tons of ilmenite?

The production of ${\text{S}}_8$ from the ${\mathbf{\text{H}}}_{\mathbf{2}}\mathbf{ }\mathbf{\text{S}}\mathbf{(}\mathbf{ }\mathbf{\text{g}}\mathbf{)}$ for step 2, found in natural gas deposits occurs through the Claus process (Section 22.5):

(a) Use these two unbalanced steps to write an overall balanced equation for this process:

1. ${\mathbf{\text{H}}}_{\mathbf{\text{2}}}{\mathbf{\text{S(g) + O}}}_{\mathbf{\text{2}}}\mathbf{\text{(g)}}\mathbf{\to }{\mathbf{\text{S}}}_{\mathbf{\text{8}}}{\mathbf{\text{(g) + SO}}}_{\mathbf{\text{2}}}{\mathbf{\text{(g) + H}}}_{\mathbf{\text{2}}}\mathbf{\text{O(g)}}$
   
2. ${\mathbf{\text{H}}}_{\mathbf{\text{2}}}{\mathbf{\text{S(g) + SO}}}_{\mathbf{\text{2}}}\mathbf{\text{(g)}}\mathbf{\to }{\mathbf{\text{S}}}_{\mathbf{\text{8}}}{\mathbf{\text{(g) + H}}}_{\mathbf{\text{2}}}\mathbf{\text{O(g))}}$
   (b)  Write the overall reaction with ${\mathbf{\text{Cl}}}_{\mathbf{\text{2}}}$ as the oxidizing agent instead of ${\mathbf{\text{O}}}_{\mathbf{\text{2}}}$. Use thermodynamic data to show whether ${\mathbf{\text{Cl}}}_{\mathbf{\text{2}}}\left(g\right)$ can be used to oxidize  ${\mathbf{\text{H}}}_{\mathbf{\text{2}}}\mathbf{\text{S(g).}}$
   (c) Why is oxidation by  preferred to oxidation by  ${\mathbf{\text{Cl}}}_{\mathbf{\text{2}}}$?

Question: Acid mine drainage (AMD) occurs when geologic deposits containing pyrite  are exposed to oxygen and moisture. AMD is generated in a multistep process catalysed by acidophilic (acid-loving) bacteria. Balance each step and identify those that increase acidity:

1.  ${\mathbf{\text{FeS}}}_{\mathbf{\text{2}}}{\mathbf{\text{(s) + O}}}_{\mathbf{\text{2}}}\mathbf{\text{(g)}}\mathbf{\to }{\mathbf{\text{Fe}}}^{\mathbf{\text{2 + }}}\mathbf{\text{(aq) + S}}{{\mathbf{\text{O}}}_{\mathbf{\text{4}}}}^{\mathbf{\text{2 - }}}\mathbf{\text{(aq)}}$
2.  ${\mathbf{\text{Fe}}}^{\mathbf{\text{2 + }}}{\mathbf{\text{(aq) + O}}}_{\mathbf{\text{2}}}\mathbf{\text{(g)}}\mathbf{\to }{\mathbf{\text{Fe}}}^{\mathbf{\text{3 + }}}{\mathbf{\text{(aq) + H}}}_{\mathbf{\text{2}}}\mathbf{\text{O(l)}}$
3.  ${\mathbf{\text{Fe}}}^{\mathbf{\text{3 + }}}{\mathbf{\text{(aq) + H}}}_{\mathbf{\text{2}}}\mathbf{\text{O(l)}}\mathbf{\to }{\mathbf{\text{Fe(OH)}}}_{\mathbf{\text{3}}}{\mathbf{\text{(s) + 12H}}}^{\mathbf{\text{ + }}}\mathbf{\text{(aq)}}$
4.   ${\mathbf{\text{FeS}}}_{\mathbf{\text{2}}}{\mathbf{\text{(s) + Fe}}}^{\mathbf{\text{3 + }}}\mathbf{\text{(aq)}}\mathbf{\to }{\mathbf{\text{Fe}}}^{\mathbf{\text{2 + }}}\mathbf{\text{(aq) + S}}{{\mathbf{\text{O}}}_{\mathbf{\text{4}}}}^{\mathbf{\text{2 - }}}\mathbf{\text{(aq)}}$

The lead(IV) oxide used in car batteries is prepared by coating the electrode plate with PbO and then oxidizing it to lead dioxide (${\mathbf{\text{PbO}}}_{\mathbf{\text{2}}}$). Despite its name,  ${\mathbf{\text{PbO}}}_{\mathbf{\text{2}}}$has a nonstoichiometric ratio of lead to oxygen of about . In fact, the holes in the${\mathbf{\text{PbO}}}_{\mathbf{\text{2}}}$  crystal structure due to missing O atoms are responsible for the oxide’s conductivity. (a) What is the mole % of O missing from the  ${\mathbf{\text{PbO}}}_{\mathbf{\text{2}}}$structure? (b) What is the molar mass of the nonstoichiometric compound?

How does acid rain affect the leaching of phosphate into groundwater from terrestrial phosphate rock? Calculate the solubility of ${\mathbf{\text{Ca}}}_{\mathbf{\text{3}}}{\mathbf{\text{(PO}}}_{\mathbf{\text{4}}}{\mathbf{\text{)}}}_{\mathbf{\text{2}}}$ in each of the following: (a) Pure water, pH  (Assume that $\mathbf{\text{P}}{{\mathbf{\text{O}}}_{\mathbf{\text{4}}}}^{\mathbf{\text{3 - }}}$ does not react with water.) (b) Moderately acidic rainwater, pH  $\mathbf{\text{4.5}}$(Hint: Assume that all the phosphate exists in the form that predominates at this pH.)

Ores with as little as  $\mathbf{\text{0.25\% }}$ by mass of copper are used as sources of the metal. (a) How many kilograms of such an ore would be needed for another Statue of Liberty, which contains  $\mathbf{2}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{5}}$ lb of copper? (b) If the mineral in the ore is chalcopyrite (${\mathbf{\text{FeCuS}}}_{\mathbf{\text{2}}}$), what is the mass % of chalcopyrite in the ore?

Even though most metal sulphides are sparingly soluble in water, their solubilities differ by several orders of magnitude. This difference is sometimes used to separate the metals by con pH. Use the following data to find the pH at which you can separate $\mathbf{\text{0.10}}$ M  ${\mathbf{\text{Cu}}}^{\mathbf{\text{2 + }}}$and $\mathbf{\text{0.10}}$ M${\mathbf{\text{Ni}}}^{\mathbf{\text{2 + }}}$ : Saturated ${\mathbf{\text{H}}}_{\mathbf{\text{2}}}\mathbf{\text{S}}$=0.10M

$$\begin{gathered} {\mathbf{\text{K}}}_{\mathbf{\text{a1}}}{\mathbf{\text{ of H}}}_{\mathbf{\text{2}}}{\mathbf{\text{S = 9×10}}}^{\mathbf{-}\mathbf{8}} \\ {\mathbf{\text{K}}}_{\mathbf{\text{a2}}}{\mathbf{\text{ of H}}}_{\mathbf{\text{2}}}\mathbf{\text{S = 1}}{\mathbf{\times 10}}^{\mathbf{-}\mathbf{17}} \\ {\mathbf{\text{K}}}_{\mathbf{\text{sp}}}\mathbf{\text{ of NiS=1.1}}{\mathbf{\times 10}}^{\mathbf{-}\mathbf{18}} \\ {\mathbf{\text{K}}}_{\mathbf{\text{sp}}}\mathbf{\text{ of CuS = 8}}{\mathbf{\times 10}}^{\mathbf{-}\mathbf{34}} \end{gathered}$$

Like heavy water (${\mathbf{\text{D}}}_{\mathbf{\text{2}}}\mathbf{\text{O}}$), so-called “semi-heavy water” (HDO) undergoes H/D exchange. The scenes below depict an initial mixture of HDO and ${\mathbf{\text{H}}}_{\mathbf{\text{2}}}$ reaching equilibrium.

World production of chromite $\left({\text{FeCr}}_{\text{2}}{\text{O}}_{\text{4}}\right)$ , the main ore of chromium, was  ${\mathbf{\text{1.5×10}}}^{\mathbf{\text{7}}}$ metric tons in $\mathbf{2003}$ . To isolate chromium, a mixture of chromite and sodium carbonate is heated in air to form sodium chromate, iron(III) oxide, and carbon dioxide. The sodium chromate is dissolved in water, and this solution is acidified with sulfuric acid to produce the less soluble sodium dichromate. The sodium dichromate is filtered out and reduced with carbon to produce chromium(III) oxide, sodium carbonate, and carbon monoxide. The chromium(III) oxide is then reduced to chromium with aluminium metal. (a) Write balanced equations for each step. (b) What mass of chromium (in kg) could be prepared from the $\mathbf{2003}$  world production of chromite?

The overall cell reaction for aluminium production is 

${\mathbf{\text{2Al}}}_{\mathbf{\text{2}}}{\mathbf{\text{O}}}_{\mathbf{\text{3}}}(\text{in }\left.{\text{Na}}_{\text{3}}{\text{AlF}}_{\text{6}}\right)\mathbf{\text{ + 3C(graphite)}}\mathbf{\to }\mathbf{\text{4Al(}}\mathit{\ell }{\mathbf{\text{) + 3CO}}}_{\mathbf{\text{2}}}\mathbf{\text{(g)}}$

(a) Assuming 100% efficiency, how many metric tons (t) of ${\mathbf{\text{Al}}}_{\mathbf{\text{2}}}{\mathbf{\text{O}}}_{\mathbf{\text{3}}}$ are consumed per metric ton of $\mathit{A}\mathit{I}$ produced? (b) Assuming 100% efficiency, how many metric tons of the graphite anode are consumed per metric ton of  produced? (c) Actual conditions in an aluminium plant require 1.89t of ${\mathbf{\text{Al}}}_{\mathbf{\text{2}}}{\mathbf{\text{O}}}_{\mathbf{\text{3}}}$ and 0.45t of graphite per metric ton of$\mathit{A}\mathit{I}$ . What is the percent yield of  with respect to ${\mathbf{\text{Al}}}_{\mathbf{\text{2}}}{\mathbf{\text{O}}}_{\mathbf{\text{3}}}$? (d) What is the percent yield of$\mathit{A}\mathit{I}$  with respect to graphite? (e) What volume of  ${\mathbf{\text{CO}}}_{\mathbf{\text{2}}}{\mathbf{\text{(in m}}}^{\mathbf{\text{3}}}\mathbf{\text{)}}$is produced per metric ton of  $\mathit{A}\mathit{I}$at operating conditions of  ${\mathbf{960}}^{\mathbf{°}}\mathit{C}$and exactly1atm?

The disproportionation of to graphite and ${\mathbf{\text{CO}}}_{\mathbf{\text{2}}}$is thermodynamically favoured but slow. (a) What does this mean in terms of the magnitudes of the equilibrium constant (K), rate c$\mathbf{\text{CO}}$onstant (k), and activation energy $\left({\text{E}}_{\text{a}}\right)$? (b) Write a balanced equation for the disproportionation of $\mathbf{\text{CO}}$. (c) Calculate   at ${\mathbf{\text{K}}}_{\mathbf{\text{c}}}$. (d) Calculate at${\mathbf{\text{K}}}_{\mathit{P}}$ .

Because of their different molar masses, ${\mathbf{\text{H}}}_{\mathbf{\text{2}}}$ and  ${\mathit{D}}_{\mathbf{\text{2}}}$effuse at different rates (Section ).

 (a) If it takes$\mathbf{\text{16.5}}$ min for $\mathbf{\text{0.10mol}}$of ${\mathbf{\text{H}}}_{\mathbf{\text{2}}}$to effuse, how long does it take for$\mathbf{0}\mathbf{.}\mathbf{10}\mathbf{ }\mathit{m}\mathit{o}\mathit{l}$  of${\mathit{D}}_{\mathbf{\text{2}}}$ to do so in the same apparatus at the same and ? (b) How many effusion steps does it take to separate an equimolar mixture of${\mathit{D}}_{\mathbf{\text{2}}}$ and ${\mathbf{\text{H}}}_{\mathbf{\text{2}}}$to$\mathbf{99}\mathit{m}\mathit{o}\mathit{l}\mathbf{\%}$ purity?

Question: Chemosynthetic bacteria reduce ${\mathbf{CO}}_{\mathbf{2}}$  by “splitting” ${\mathbf{H}}_{\mathbf{2}}\mathbf{S}\mathbf{ }\left(g\right)$instead of the ${\mathbf{H}}_{\mathbf{2}}\mathbf{O}\mathbf{\left(}\mathbf{g}\mathbf{\right)}$used by photosynthetic organisms. Compare the free energy change for splitting ${\mathbf{H}}_{\mathbf{2}}\mathbf{S}$with that for splitting ${\mathbf{H}}_{\mathbf{2}}\mathbf{O}$ . Is there an advantage to using  ${\mathbf{H}}_{\mathbf{2}}\mathbf{S}$ instead of ${\mathbf{H}}_{\mathbf{2}}\mathbf{O}$?

Question: Silver has a face-cantered cubic structure with a unit cell edge length of $\mathbf{408}\mathbf{.}\mathbf{6}\mathbf{ }\mathbf{pm}$. Sterling silver is a substitutional alloy that contains $\mathbf{7}\mathbf{.}\mathbf{5}\mathbf{\%}$copper atoms. Assuming the unit cell remains the same, find the density of silver and of sterling silver.

Question: Earth’s mass is estimated to be $\mathbf{5}\mathbf{.}\mathbf{98}\mathbf{\times }{\mathbf{10}}^{\mathbf{24}}\mathbf{ }\mathbf{kg}$, and titanium represents $\mathbf{0}\mathbf{.}\mathbf{05}\mathbf{\%}$ by mass of this total. (a) How many moles of  are present? (b) If half of the $\mathbf{Ti}$ is found as ilmenite $\mathbf{\left(}{\mathbf{FeTiO}}_{\mathbf{3}}\mathbf{\right)}$, what mass of ilmenite is present? (c) If the airline and auto industries use $\mathbf{1}\mathbf{.}\mathbf{00}\mathbf{\times }{\mathbf{10}}^{\mathbf{5}}$tons of $\mathbf{Ti}$ per year, how many years would it take to use up all the $\mathbf{Ti}\mathbf{ }\left(1\mathrm{ton}\times 2000 \mathrm{lb}\right)$ ?  

Question:  In 1790, Nicolas Leblanc found a way to form   from . His process, now obsolete, consisted of three steps obsolete, consisted of three steps: 

 $$\begin{gathered} \mathbf{2}\mathbf{NaCl}\mathbf{\left(}\mathbf{s}\mathbf{\right)}\mathbf{+}{\mathbf{H}}_{\mathbf{2}}{\mathbf{SO}}_{\mathbf{4}}\mathbf{\left(}\mathbf{aq}\mathbf{\right)}\mathbf{\to }{\mathbf{Na}}_{\mathbf{2}}{\mathbf{SO}}_{\mathbf{4}}\mathbf{\left(}\mathbf{aq}\mathbf{\right)}\mathbf{+}\mathbf{2}\mathbf{HCl}\mathbf{\left(}\mathbf{g}\mathbf{\right)} \\ {\mathbf{Na}}_{\mathbf{2}}{\mathbf{SO}}_{\mathbf{4}}\mathbf{\left(}\mathbf{aq}\mathbf{\right)}\mathbf{+}\mathbf{2}\mathbf{C}\mathbf{\left(}\mathbf{s}\mathbf{\right)}\mathbf{\to }{\mathbf{Na}}_{\mathbf{2}}\mathbf{S}\mathbf{\left(}\mathbf{aq}\mathbf{\right)}\mathbf{+}\mathbf{2}{\mathbf{CO}}_{\mathbf{2}}\mathbf{\left(}\mathbf{g}\mathbf{\right)} \\ {\mathbf{Na}}_{\mathbf{2}}\mathbf{S}\mathbf{\left(}\mathbf{aq}\mathbf{\right)}\mathbf{+}{\mathbf{CaCO}}_{\mathbf{3}}\mathbf{\left(}\mathbf{s}\mathbf{\right)}\mathbf{\to }{\mathbf{Na}}_{\mathbf{2}}{\mathbf{CO}}_{\mathbf{3}}\mathbf{\left(}\mathbf{s}\mathbf{\right)}\mathbf{+}\mathbf{CaS}\mathbf{\left(}\mathbf{s}\mathbf{\right)} \end{gathered}$$

1. Write a balanced overall equation for the process.
2. Calculate the ${\mathbf{H}}^{\mathbf{0}}$of $\mathbf{CaS}$ if ${\mathbf{H}}_{\mathbf{rxn}}^{\mathbf{\circ }}$ is$\mathbf{351}\mathbf{.}\mathbf{8}\mathbf{ }\mathbf{kJ}\mathbf{/}\mathbf{mol}$
3. Is the overall process spontaneous at standard-state conditions and$\mathbf{298}\mathbf{ }\mathbf{K}$ ?
4.  How many grams of ${\mathbf{Na}}_{\mathbf{2}}{\mathbf{CO}}_{\mathbf{3}}$ form $\mathbf{250}\mathbf{ }\mathbf{g}$of $\mathbf{NaCl}$ if the process is 73% efficient?

Question: Limestone ${\mathbf{CaCO}}_{\mathbf{3}}$ is the second most abundant mineral on Earth after SiO2. For many uses, it is first decomposed thermally to quicklime$\mathbf{CaO}$.$\mathbf{MgO}$ is prepared similarly from${\mathbf{MgCO}}_{\mathbf{3}}$.

(a) At what T is each decomposition spontaneous? 

(b) Quicklime reacts with ${\mathbf{SiO}}_{\mathbf{2}}$ to form a slag ${\mathbf{CaSiO}}_{\mathbf{3}}$, a byproduct of steelmaking. In 2003, the total steelmaking capacity of the U.S. steel industry was 2,370,000 tons per week, but only 84% of this capacity was utilized. If $\mathbf{50}\mathbf{.}\mathbf{0}\mathbf{ }\mathbf{kg}$of slag is produced per ton of steel, what mass (in kg) of limestone was used to make slag in 2003?